Question

# In unit-vector notation, what is the net torque about the origin on a flea located at coordinates (0, -4.0 m, 5.0 m) when forces${\overrightarrow{F_1}} = (3.0\ N){\hat{k}}$and${\overrightarrow{F_2}} = (-2.0\ N){\hat{j}}$act on the flea?

Solution

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$\textbf{Givens:}$

The flea located at $(0, -4\text{ m } , 5 -4\text{ m })$.

The forces are $F_1 = 3\hat{k}$ N and $F_2 = -2\hat{j}$ N.

Torque can be defined as

$\begin{gather*} \vec{\tau} = \vec{r}\times \vec{F} \end{gather*}$

Where r and F are the position vector and the force vector, respectively.

Substitute the givens

\begin{align*} \vec{\tau} &= ( -4 \hat{j} + 5 \hat{k} ) \times ( -2 \hat{j} + 3 \hat{k} )\\ & = -12 \hat{j} .\hat{k} - 10 \hat{k}.\hat{j} \\ & = -12 \hat{i} + 10 \hat{i}\\ & =( -2 \hat{i}) \text{ N.m } \end{align*}

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